Combining Texts

All the ideas for 'fragments/reports', 'Higher-Order Logic' and 'Philosophy'

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24 ideas

3. Truth / A. Truth Problems / 4. Uses of Truth
20320 Truth is what unites, and the profound truths create a community [Jaspers]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
16. Persons / F. Free Will / 2. Sources of Free Will
20323 Freedom needs knowledge, the possibility of arbitrariness, and law [Jaspers]
16. Persons / F. Free Will / 4. For Free Will
20322 I am aware that freedom is possible, and the freedom is not in theory, but in seeking freedom [Jaspers]
20. Action / C. Motives for Action / 4. Responsibility for Actions
20324 My freedom increases as I broaden my vision of possiblities and motives [Jaspers]
23. Ethics / A. Egoism / 1. Ethical Egoism
3031 The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius]
23. Ethics / F. Existentialism / 1. Existentialism
20321 The struggle for Existenz is between people who are equals, and are utterly honest [Jaspers]
20318 My helplessness in philosophising reveals my being, and begins its upsurge [Jaspers]
20325 Once we grasp freedom 'from' things, then freedom 'for' things becomes urgent [Jaspers]
23. Ethics / F. Existentialism / 6. Authentic Self
20315 'Existenz' is the potential being, which I could have, and ought to have [Jaspers]
20317 Mundane existence is general, falling under universals, but Existens is unique to individuals [Jaspers]
20319 We want the correct grasp on being that is neither solipsism nor absorption in the crowd [Jaspers]
23. Ethics / F. Existentialism / 7. Existential Action
20316 Every decision I make moves towards or away from fulfilled Existenz [Jaspers]